Question

Find each result using any method you like. \(67 \%\) of 250

Short answer

167.5

Step-by-step solution

- Understand the meaning of the percentage

A percentage represents a portion of 100. For example, 67% means 67 out of every 100. To find 67% of a number, convert the percentage to a decimal.

- Convert the percentage to a decimal

Convert 67% to a decimal by dividing by 100: \[ 67\text{\textdivide}100 = 0.67 \]

- Multiply by the given number

Multiply the decimal by the given number to find the percentage of that number. In this case: \[ 0.67 \times 250 = 167.5 \]

Key concepts

percentage to decimal conversion

To solve percentage problems like finding 67% of 250, you need to start with converting the percentage to a decimal. This step is crucial because it makes calculations easier and more straightforward.
A percentage is essentially a fraction out of 100. So, to convert a percentage to a decimal, you divide by 100.
For example, converting 67% to a decimal is done as follows:
\( 67\text{\textdivide}100 = 0.67 \)
This conversion helps in simplifying the multiplication process. It is a standard method that can be applied to any percentage, making it an essential skill for various math problems. Remember:

• Move the decimal point two places to the left.
• Add zeros if necessary to complete the shift for better accuracy.

With this understanding, you're equipped to tackle the next mathematical step with ease.

multiplication

After converting the percentage to a decimal, the next step is multiplication. Multiplication is straightforward but crucial because it directly impacts the accuracy of your result.
In our example, we've converted 67% to 0.67. Now, we multiply 0.67 by the given number, which is 250:
\( 0.67 \times 250 = 167.5 \)
Here's a step-by-step breakdown:

• Write down the two numbers to be multiplied.
• Multiply the numbers as if they were whole numbers.
• Place the decimal in the product. The number of decimal places in the result is the sum of the decimal places in the original numbers.

Multiplication of decimals may seem tricky, but with practice, it becomes a lot easier. Keep in mind:

• Align the numbers by their rightmost digits.
• Ignore the decimals during the multiplication and reinsert them in the final product.

By maintaining accuracy in this step, you ensure your final result is correct.

mathematical steps

Understanding and applying the correct mathematical steps is crucial in solving percentage problems. This involves breaking the problem down into manageable parts and solving each part methodically.
Here are the steps in our example:

• Understand the problem: Know that finding 67% of 250 means calculating a portion of 250.
• Convert the percentage to a decimal: Divide 67 by 100 to get 0.67.
• Multiply by the given number: Multiply 0.67 by 250 to get 167.5.

Breaking the problem into these specific steps helps in maintaining accuracy and clarity.

• Always start by understanding what the percentage means.
• Convert that percentage into a simpler form like a decimal.
• Use multiplication to find the desired portion.

Following these structured mathematical steps ensures that you don't skip any part, leading to a correct and easy-to-follow solution. Additionally, practicing these steps repeatedly builds confidence and proficiency in solving similar math problems.